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Physical Review A

Controlling the intensity statistics of speckle patterns: From normal to subthermal or superthermal distributions

Samuel B. Alves, Hugo L. D. de S. Cavalcante, Gilson F. de Oliveira, Thierry Passerat de Silans, Itamar Vidal, Martine Chevrollier, Marcos Oriá

Published Mar 19, 2019• 11 citations
Publisher

Abstract

We study the propagation of speckle patterns in a tunable nonlinear medium. Starting from a spatial pattern of photons with a normal distribution (speckle field), we characterize the evolution of the radiation to either subthermal or superthermal distributions and demonstrate the control of this evolution through a single parameter. Our experimental control of the local degree of coherence of the output photons is well described by numerical simulations that consider both dispersive and absorptive nonlinear effects. Particularly, we analyze the role of the nonlinear absorption that either enhances or competes with the dispersive effects in the evolution of speckle fields. In some realizations, an asymptotic power law is observed in the photon spatial distribution.

DOI
10.1103/physreva.99.033838

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We study the propagation of speckle patterns in a tunable nonlinear medium. Starting from a spatial pattern of photons with a normal distribution (speckle field), we characterize the evolution of the radiation to either subthermal or superthermal distributions and demonstrate the control of this evolution through a single parameter. Our experimental control of the local degree of coherence of the output photons is well described by numerical simulations that consider both dispersive and absorptive nonlinear effects. Particularly, we analyze the role of the nonlinear absorption that either enhances or competes with the dispersive effects in the evolution of speckle fields. In some realizations, an asymptotic power law is observed in the photon spatial distribution.
We investigate the transformation of Rayleigh speckle patterns by an atomic cesium vapor. After propagation through the atomic vapor, the incident exponentially decaying intensity distribution of the Rayleigh speckles is transformed with enhancement of high intensities probabilities (extreme events). The measured intensity distributions are fitted by Weibull distributions. The nonlinear interaction between the atomic vapor and the optical field leads to intensity-dependent refraction and absorption, resulting in changes of the speckle spots' intensities with propagation. We measure the inverse of the shape parameter of the Weibull distributions as a function of laser detuning and interpret the results by modeling the speckle propagation.
We provide a theoretical explanation of the results on the intensity distributions and correlation functions obtained from a random-beam speckle field in nonlinear bulk waveguides reported in the recent publication by Bromberg et al. [Nat. Photonics 4, 721 (2010)]. We study both the focusing and defocusing cases and in the limit of small speckle size (short-correlated disordered beam) provide analytical asymptotes for the intensity probability distributions at the output facet. Additionally we provide a simple relation between the speckle sizes at the input and output of a focusing nonlinear waveguide. The results are of practical significance for nonlinear Hanbury Brown and Twiss interferometry in both optical waveguides and Bose-Einstein condensates.
We consider the propagation of several entangled photons through an elastically scattering medium and study statistical properties of their speckle patterns. We find the spatial correlations of multiphoton speckles and their sensitivity to changes of system parameters. Our analysis covers both the directed-wave regime, where rays propagate almost ballistically while experiencing small-angle diffusion, and the real-space diffusive regime. We demonstrate that long-range correlations of the speckle patterns dominate experimental signatures for large-aperture photon detectors. We also show that speckle sensitivity depends strongly on the number of photons NNN in the incoming beam, increasing as N\sqrt{N}N​ in the directed-wave regime and as NNN in the diffusive regime.
We experimentally study the statistics of two-photon speckle patterns, obtained when spatially entangled photon pairs are scattered through a random medium. Striking differences arise between the scattering of highly entangled states and almost separable states. Both the purity of the field and the Schmidt number, which quantifies the number of entangled modes, can be obtained from the visibility of the speckles. We observe nonexponential statistics for both the intensities and the two-photon correlations.
The irradiation of a dilute cloud of cold atoms with a coherent light field produces a random intensity distribution known as laser speckle. Its statistical fluctuations contain information about the mesoscopic scattering processes at work inside the disordered medium. Following up on earlier work by Assaf and Akkermans [Phys. Rev. Lett. 98, 083601 (2007)], we analyze how static speckle-intensity correlations are affected by an internal Zeeman degeneracy of the scattering atoms. It is proven on general grounds that the speckle correlations cannot exceed the standard Rayleigh law. On the contrary, because which-path information is stored in the internal atomic states, the intensity correlations suffer from strong decoherence and become exponentially small in the diffusive regime applicable to an optically thick cloud.
Nonlinear self-action of light fields in a layer of cubic nonlinear medium can serve as a convenient tool for controllable coherence manipulation. In the present work this scheme is considered for partially coherent input light. Due to experimental requirements, we consider the model of multimode laser. For the purely phase statistics of the input beam (when the average intensity can be represented in factorized form I(r,t) equals I(r)I(t)), it is possible to find out rather simply the dependence of the effective number of (coherent) modes in output radiation on the input number of modes and the nonlinearity parameter.